What I'm having trouble understanding is since Bryan worked on the first two movies and on First Class, why was there no continuity in the Mystique look. You would think they would have catalogued all the details of what hue of blue to use, how it's applied and all that other stuff. And how hard would it have been to use the same team that did Rebecca's?

Well its been a long time since he worked in a X-Men movie and the costume department probably didn't have the same color of paint that X1/X2/X3 Mystique had. Even if the change of color looks so obvious, its not really a big concern to the crew unless the director told them to change it. And I don't think Bryan Singer is very detailed with how his characters look like in the movie.